Answer a bc by the deni5on of set minus a bc

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Unformatted text preview: CSCE 235 Combinatorics 10 PIE Theorem: Example 2 •  To illustrate, when n=4, we have |A1∪A2∪A3∪A4|= |A1|+|A2|+|A3|+|A4| - [|A1∩A2|+|A1∩A3|+|A1∩A4| +|A2∩A3|+|A2∩A4|+|A3∩A4|] + [|A1∩A2∩A3|+|A1∩A2∩A4| +|A1∩A3∩A4|+|A2∩A3∩A4|] - |A1 ∩A2 ∩A3 ∩A4| CSCE 235 Combinatorics 11 Applica5on of PIE: Example A (1) •  How many integers between 1 and 300 (inclusive) are –  Divisible by at least one of 3,5,7? –  Divisible by 3 and by 5 but not by 7? –  Divisible by 5 but by neither 3 or 7? •  Let A = {n∈Z | (1 ...
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This note was uploaded on 10/31/2013 for the course CSCE 235 taught by Professor Staff during the Spring '08 term at UNL.

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